相关论文: Invariant grids for reaction kinetics
A Cartesian grid method combined with a simplified gas kinetic scheme is presented for subsonic and supersonic viscous flow simulation on complex geometries. Under the Cartesian mesh, the computational grid points are classified into four…
This paper aims at reviewing nonlinear methods for model order reduction of structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear based…
Invariant manifolds are important constructs for the quantitative and qualitative understanding of nonlinear phenomena in dynamical systems. In nonlinear damped mechanical systems, for instance, spectral submanifolds have emerged as useful…
Model reduction methods are relevant when the computation time of a full convection-diffusion-reaction simulation based on detailed chemical reaction mechanisms is too large. In this article, we review a model reduction approach based on…
A challenge for molecular quantum dynamics (QD) calculations is the curse of dimensionality with respect to the nuclear degrees of freedom. A common approach that works especially well for fast reactive processes is to reduce the…
A novel method, the Gaussian Integral Method (GIM), is presented for calculating void fractions in Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) simulations. GIM is versatile and applicable to various grid types, including…
Grids are a general representation for capturing regularly-spaced information, but since they are uniform in space, they cannot dynamically allocate resolution to regions with varying levels of detail. There has been some exploration of…
Recently, a Riemannian proximal Newton method has been developed for optimizing problems in the form of $\min_{x\in\mathcal{M}} f(x) + \mu \|x\|_1$, where $\mathcal{M}$ is a compact embedded submanifold and $f(x)$ is smooth. Although this…
A fully adaptive methodology is developed for reducing the complexity of large dissipative systems. This represents a significant step towards extracting essential physical knowledge from complex systems, by addressing the challenging…
Finite difference discretization schemes preserving a subgroup of the maximal Lie invariance group of the one-dimensional linear heat equation are determined. These invariant schemes are constructed using the invariantization procedure for…
Understanding grain-surface processes is crucial to interpreting the chemistry of the ISM. However, accurate surface chemistry models are computationally expensive and are difficult to integrate with gas-phase simulations. A new…
In this paper, we propose an adaptive finite difference scheme in order to numerically solve total variation type problems for image processing tasks. The automatic generation of the grid relies on indicators derived from a local estimation…
Model reduction of biochemical networks relies on the knowledge of slow and fast variables. We provide a geometric method, based on the Newton polytope, to identify slow variables of a biochemical network with polynomial rate functions. The…
The performance of machine learning models can be impacted by changes in data over time. A promising approach to address this challenge is invariant learning, with a particular focus on a method known as invariant risk minimization (IRM).…
Kinetic transport equations are notoriously difficult to simulate because of their complex multiscale behaviors and the need to numerically resolve a high dimensional probability density function. Past literature has focused on building…
We derive a reduction formula for singularly perturbed ordinary differential equations (in the sense of Tikhonov and Fenichel) with a known parameterization of the critical manifold. No a priori assumptions concerning separation of slow and…
This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…
Deep learning is a potential approach to automatically develop kinetic models from experimental data. We propose a deep neural network model of KiNet to represent chemical kinetics. KiNet takes the current composition states and predicts…
This work proposes a hyper-reduction method for nonlinear parametric dynamical systems characterized by gradient fields such as Hamiltonian systems and gradient flows. The gradient structure is associated with conservation of invariants or…
We present a symbolic algorithmic approach that allows to compute invariant manifolds and corresponding reduced systems for differential equations modeling biological networks which comprise chemical reaction networks for cellular…